Hi Erwin,
probably the SWMenuPro is not compatible with mobile or has some issues to working fine.
By the way you have not to use it at all with Responsivizer to render the menu, Responsivizer has its built in mobile menu already optimized for touch devices. Just create a new menu module instance and assign it for example to the position 'responsivizer_mainmenu'. That's all.
In the pdf docs you find detailed informations about all types of menu that Responsivizer is capable to render, including the top and side slide menu, also visible in the demo area
http://demo.storejextensions.org/responsivizer
Hope this is helpful!
John